This paper proposes two global task assignments for load balancing and task fairness, and then evaluates them by computer simulation. These assignments target large tasks. One uses a distributed sorting algorithm such that a larger task is assigned to a server with a lower load, the other works on a logical ring and performs in such a way that all unassigned tasks flow around the ring and a free server accepts a new task with the highest priority from the unassigned tasks that it receives. As a result, these task assignments perform better than conventional task assignments or load balancing with respect to both the mean response time and the task fairness, especially for large networks. Moreover, these task assignments do not require much memory space even if the network becomes very large thus making them suitable for execution in a large network.
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